As is known in the art, system dynamics modeling is an approach to studying the behavior of complex systems over time using feedback loops and delays. System dynamics modeling has found application in a wide range of areas including economics, epidemiology, population growth, ecological systems, and more.
System dynamics modeling generally begins by defining a problem to be studied or analyzed, for example, how to allocate a company's limited resources for a new product launch. The modeler defines stocks or entities which are increased or decreased during the simulation. For example, for the new product launch simulation, two types of consumers can be defined as stocks; (1) potential purchasers, and (2) new purchasers.
Next, the modeler defines flows of the simulation, for example, flows of consumers from potential purchasers to new purchasers. The modeler also defines feedback mechanisms which affect the stocks and flows. For example, advertising and word of mouth in the market may affect the flow rate. In particular, as more consumers become aware of the product either via advertising programs or through word of mouth, the flow of consumers from potential purchasers to new purchasers increases. The modeler may also define various equations for determining the flow, estimating parameters, and identifying initial conditions.
After the modeler tests and verifies the models, the modeler may perform various “what if” scenarios to better understand the dynamics of the models and to control the output. As is also known in the art, modelers may use computer software programs to build, simulate, and analyze system dynamics models. One such computer software program is Vensim® from Ventana Systems, Inc.
FIG. 1 illustrates a conventional prior art system dynamics model 100 for a complex system. The complex system relates to market dynamics for a company's product introduction, similar to the new product launch described above. Potential adopters 102 include the consumers who may purchase the product. Adopters 104 include the consumers who have purchased the product. New adopters 106 represent the rate of consumer adoption of the product, i.e., the increase or decrease in product purchasing by consumers.
Typically, potential adopters 102 and adopters 104 are referred to as model entities or stocks which accumulate or deplete over time. In this example, the stock of potential adopters 102 will decrease as the stock of adopters 104 increases. This assumes that the number of consumers remains constant over time.
New adopters 106 are referred to as the rate of change or flow in a model stock over time. In this example, the flow of new adopters 106 may increase when the product is introduced to the market as early potential adopters, known as innovators 103, rush to purchase the product. As the number of adopters 104 increases, the flow of new adopters 106 continues to increase as word of mouth about the product travels from adopters 104 to later potential adopters 102, known as followers 105. As the market begins to saturate, the flow of new adopters 106 begins to level off and may stop when the number of potential adopters is completely depleted.
During simulation, multiple versions or instances of the model are used to simulate the overall performance of the complex system. For example, a separate instance of the model may be created for each automobile on the road. The results for each separate instance are aggregated to obtain an overall system performance.
It would be desirable to provide a method of integrating system dynamics models at various levels of details, for example, by integrating non-subscripted and subscripted system dynamics model to view and analyze interactions between the various instances of the model, in addition to the overall system performance.